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geometry

3D "Basilica" Julia set
geometry

3-D Fractals Offer Clues to Complex Systems

By folding fractals into 3-D objects, a mathematical duo hopes to gain new insight into simple equations.

Abstractions blog

Air Traffic Control for Random Surfaces

Mathematicians have had a hard time finding commonalities in large groups of random shapes — until recently.

geometry

A Unified Theory of Randomness

Researchers have uncovered deep connections among different types of random objects, illuminating hidden geometric structures.

Abstractions blog

Handicapping the 2018 Fields Medal

Peter Scholze is a favorite to win one of the highest honors in mathematics for his contributions in number theory and geometry.

profile

The Oracle of Arithmetic

At 28, Peter Scholze is uncovering deep connections between number theory and geometry.

geometry

Sphere Packing Solved in Higher Dimensions

The Ukrainian mathematician Maryna Viazovska has solved the centuries-old sphere-packing problem in dimensions eight and 24.

insights puzzle

Solution: ‘The Problem With Dancing Shapes’

Assigning elements from a large collection to one of two categories can yield almost “magical” predictions about highly complicated problems without actually solving them.

insights puzzle

The Problem With Dancing Shapes

In a geometrically designed social club, how do dancing, triangles and hexagons mix?

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A Life in Games

The mathematician John Horton Conway’s myriad accomplishments — including the Game of Life, sprouts and the surreal numbers — are the product of a mind at play.